How to find the endpoints of a line segment

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GRE Quantitative Reasoning › How to find the endpoints of a line segment

Questions 1 - 4

1

What is the other endpoint of a line segment with one point that is and a midpoint of ?

Explanation

Recall that the midpoint formula is like finding the average of the and values for two points. For two points and , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for . We know:

$\left(\frac{6+c}{2},\frac{8+d}{2}\right)=(14,1)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{6+c}{2} = 14$

Y-Coordinate:

$\frac{8+d}{2}=1$

Therefore, our point is

2

What is the other endpoint of a line segment with one point that is and a midpoint of ?

Explanation

What is the other endpoint of a line segment with one point that is and a midpoint of ?

Recall that the midpoint formula is like finding the average of the and values for two points. For two points and , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for . We know:

$\left(\frac{-15+c}{2},\frac{14+d}{2}\right)=(-19,4)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{-15+c}{2}=-19$

Y-Coordinate:

$\frac{14+d}{2}=4$

Therefore, our point is

3

There is a line defined by two end-points, and . The midpoint between these two points is . What is the value of the point ?

Explanation

Recall that to find the midpoint of two points and , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\left(\frac{11+a}{2},\frac{-5+b}{2}\right)=(-6,-21)$

You merely need to solve each coordinate for its respective value.

$\frac{11+a}{2}=-6$

Then, for the y-coordinate:

$\frac{-5+b}{2}=-21$

Therefore, our other point is:

4

There is a line defined by two end-points, and . The midpoint between these two points is . What is the value of the point ?

Explanation

Recall that to find the midpoint of two points and , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\left(\frac{4+a}{2},\frac{3+b}{2}\right)=(7,15)$

You merely need to solve each coordinate for its respective value.

$\frac{4+a}{2}=7$

Then, for the y-coordinate:

$\frac{3+b}{2}=15$

Therefore, our other point is:

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